Heat transfer characteristics of thin power-law liquid films over horizontal stretching sheet with internal heating and variable thermal coefficient
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The effect of internal heating source on the film momentum and thermal transport characteristic of thin finite power-law liquids over an accelerating unsteady horizontal stretched interface is studied. Unlike most classical works in this field, a general surface temperature distribution of the liquid film and the generalized Fourier’s law for varying thermal conductivity are taken into consideration. Appropriate similarity transformations are used to convert the strongly nonlinear governing partial differential equations (PDEs) into a boundary value problem with a group of two-point ordinary differential equations (ODEs). The correspondence between the liquid film thickness and the unsteadiness parameter is derived with the BVP4C program in MATLAB. Numerical solutions to the self-similarity ODEs are obtained using the shooting technique combined with a Runge-Kutta iteration program and Newton’s scheme. The effects of the involved physical parameters on the fluid’s horizontal velocity and temperature distribution are presented and discussed.
Key wordsnon-Newtonian fluid nonlinear equation thin film heat transfer internal heating stretching sheet thermal conductivity numerical solution
- a, b
positive constant, s-1
specific heat capacity, J · kg-1 · K-1
positive constant, m-r1
dimensionless stream function
liquid film thickness, m
viscosity coefficient, kg · m-1 · sn-2
effective thermal conductivity, W· m-1 · K-1
generalized Prandtl number
local Reynolds number
r 2, power indices
temperature at origin, K
standard temperature, K
temperature of stretched surface, K
- u, v
liquid velocity components along with x-direction and y-direction, respectively, m · s-1
horizontal velocity of stretched surface, m · s-1
- x, y
streamwise coordinate and cross-stream coordinate, respectively, m.
dimensionless film thickness
density, kg · m-3
modified shear viscous drag, N · m-2
heating source parameter
stream function, m2 · s-1
consistency thermal coefficient, kg · m · sn-4 · K-1 s, for wall surface or stretched surface.
Chinese Library ClassificationO35 O373
2010 Mathematics Subject Classification76A05 76A20 80A20 34B15
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- Elgazery, N. S. and Hassan, M. A. The effects of variable fluid properties and magnetic field on the flow of non-Newtonian fluid film on an unsteady stretching sheet through a porous medium. Communications in Numerical Methods in Engineering, 24, 2113–2129 (2008)MathSciNetCrossRefzbMATHGoogle Scholar